• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.215-222
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• 2000

A multigrid algorithm is developed for solving the one- dimensional initial boundary value problem. The numerical solutions of linear and nonlinear Burgers; equation for various initial conditions are studied. The stability conditions are derived by Von -Neumann analysis . Numerical results are presented.

• Journal of Dental Rehabilitation and Applied Science
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• v.18 no.2
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• pp.81-91
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• 2002

Dental implant systems have shown many post-surgical problems and One of the most frequent problem is screw loosening. To reduce screw loosening, a number of methods have been tried and recently fundamental modification of fixture-abutment connection structure was developed and used the most frequently. Former implant system structure, such as Br${\aa}$nemark, had external hex with the height of 0.7 mm and later, fixture with external hex of 1.0 mm height and internal hex structure were developed. In addition, the method of morse taper application was introduced to reduce screw loosening. In this study, the level of screw loosening of each implant systems was compared based on the vibration loosening measurement of abutment screw of each implant systems. Analysis of measured value was performed using 3 kinds of methods, (i) Percentage of average of initial 3 times loosening-torque value(initial loosening value) to tightening-torque of 30 Ncm, (ii) Percentage of loosening-torque value after 200 N strength loaded(experimental value) to initial loosening value and (iii) Percentage of experimental value to 30 Ncm of tightening-torque. Each result of analyses shows the value of initial loosening, loosening by repetitive load and final loosening level. The results of this study were as follows. (1) Percentage of initial loosening value to tightening-torque was increased in order of 0.7 mm external hex, 1.0 mm external hex, internal hex and internal taper and all values between each groups showed statistical significance (p<0.05). (2) Percentage of experimental value to initial loosening value was increased in order of internal hex, 0.7 mm external hex, 1.0 mm external hex and internal taper. Value of internal taper showed significant difference with that of 0.7 mm external hex and internal hex (p<0.05). (3) Percentage of experimental value to tightening torque was increased in order of 0.7 mm external hex, 1.0 mm external hex, internal hex and internal taper. Values of all groups showed statistical significance (p<0.05) except between the groups of 1.0 mm external hex and internal hex. Based on those results, there was no significant difference of loosening-torque by repetitive loading except internal taper. It is supposed that implant system with high resistant capability against initial loosening could be recommended for clinical use. In addition, in case of single implant restoration, 1.0 mm external hex or internal hex could be recommended rather than 0.7 mm external hex, and the use of internal taper would be the most useful way to reduce screw loosening.

• The Journal of Korean Academy of Prosthodontics
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• v.43 no.5
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• pp.671-683
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• 2005

Statement of problem: The most commonly reported problem associated with dental implant restoration is the loosening of the screws. Purpose: This study compared the efficacy of an implant system incorporating an anti-rotational locking sleeve(Anti-Rotating Inner Post Screw System(ARIPS-system)) with other, traditional implant systems as a means of minimizing vibration loosening. Materials and methods: Three implant systems were examined; the conventional external hex type, the ARIPS-system, and the internal taper type implant system 30 specimens(10 samples per group)were fabricated and each abutment screw was secured to the implant future with 32Ncm of torque force and loosening torque was measured using a Torque Gauge. The procedure was repeated 3 times, recording initial loosening torque each time. The re-tightened abutment screw was subjected to a cyclic load having a maximum forte of 200N and minimum of 20N at 2Hz over a period of 12,600 cycles. after which the loosening torque was measured. Measured values were calaulated for statistical analysis. Analysis of measured value was performed by 3 methods: (i) as a percentage average of the initial 3 loosening-torque values(initial loosening value) to the tightening torque of 32Ncm, (ii) as a percentage of the loosening torque value after a load of 200N(experimental value) to the initial loosening value, and (iii) as a percentage of the experimental value to the 32Ncm of tightening torque. The analyses shows the amount of initial loosening at the screw, loosening by repetitive load and the the final loosening value. Results: The results of this study were as follows (1) Percentage of initial loosening value to tightening-torque was increased in order of external hex, ARIPS-system and internal taper and all values between each groups showed statistical significance (p<0.05). (2) Percentage of experimental value to initial loosening value was increased in order of external hex, ARIPS-system and internal taper. Value of internal taper showed significant difference with those of external hex and ARIPS-system (p<0.05). (3) Percentage of experimental value to tightening torque was increased in order of external hex, ARIPS-system and internal taper and all values between each groups showed statistical significance (p<0.05). Conclusion: The results of the analysis of the final loosening level value, which are closely correlated to clinical use, show that the ARIPS-system can be a useful means of minimizing abutment screw loosening when compared to the external hex type system. Although further clinical studies need to be made, the ARIPS-system should be considered to maximize the long-term success of the implant prosthesis.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.87-97
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• 2013

The purpose of this paper is to employ a new useful technique to solve the initial-Neumann boundary value problems for parabolic, hyperbolic and parabolic-hyperbolic equations and obtain a solution in form of infinite series. The results obtained indicate that this approach is indeed practical and efficient.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.173-181
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• 2014

In this paper, using the definition and properties of frequency measurement, we describe the properties of solutions of a difference equation as the initial value belongs to different intervals of the whole domain. We get the main result that if the initial value belongs to [-1, 1] which is different from $\frac{-1{\pm}\sqrt{5}}{2}$, then the solution defined by initial value have two frequent limits 0 and 1 of the same degree 0.5.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.15 no.25
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• pp.11-14
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• 1992

This paper presents a method for establishing an initial value of redundancy optimization problem to maximize system reliability of multiconstraint mixed parallel-series system. The constraints not be linear. This paper proposes a new initial value which is near to optimal solution by considering the relative median rate of the unreliability and amount of consumed resources for each subsystem. To show the efficiency of this model. numerical example and comparison with Narasimhalu is illustrated in chapter 4.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.331-348
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• 2018

In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.191-204
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• 2017

A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.3
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• pp.138-155
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• 2022

To solve the initial value problem we present a new single-step implicit method based on the Euler method. We prove that the proposed method has convergence order 2. In practice, numerical results of the proposed method for some selected examples show an error tendency similar to the second-order Taylor method. It can also be found that this method is useful for stiff initial value problems, even when a small number of nodes are used. In addition, we extend the proposed method by using weighted averages with a parameter and show that its convergence order becomes 2 for the parameter near $\frac{1}{2}$. Moreover, it can be seen that the extended method with properly selected values of the parameter improves the approximation error more significantly.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.